Solve: Square Root Product (√16 × √25) Plus Power of 8 Expression

Q: Why do I calculate the square roots first?

Square roots are like exponents in the order of operations! Following PEMDAS, you calculate $ \sqrt{16} = 4 $ and $ \sqrt{25} = 5 $ before any multiplication or addition.

Q: What if I don't know what 8³ equals?

Remember that $ 8^3 = 8 \times 8 \times 8 $. Calculate step by step: 8 × 8 = 64, then 64 × 8 = 512. Practice common cubes to build speed!

Q: Can I multiply the square roots first or the cube first?

Yes! Since both $ \sqrt{16} \times \sqrt{25} $ and $ 8^3 \times 3 $ are separate multiplication groups, you can calculate them in any order. Just don't add until both are complete.

Q: How do I avoid calculation errors with big numbers?

Write each step clearly: $ \sqrt{16} \times \sqrt{25} = 4 \times 5 = 20 $, then $ 8^3 \times 3 = 512 \times 3 = 1536 $, finally $ 20 + 1536 = 1556 $. Double-check each calculation!

Q: What's the fastest way to check my answer?

Estimate first: $ 4 \times 5 = 20 $ plus $ 500 \times 3 = 1500 $ ≈ 1520Your answer should be close to 15201556 is reasonable! ✓

Order of Operations with Square Roots

$\sqrt{16}\times\sqrt{25}+8^3\times3=$

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Step-by-step written solution

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Understand the problem

$\sqrt{16}\times\sqrt{25}+8^3\times3=$

Step-by-step solution

The given expression is: $\sqrt{16}\times\sqrt{25}+8^3\times3$ .

First, calculate the square roots: $\sqrt{16} = 4$ and $\sqrt{25} = 5$ .

Multiply the square roots: $4 \times 5 = 20$ .

Next, calculate the cube: $8^3 = 512$ .

Multiply the result by 3: $512 \times 3 = 1536$ .

Finally, add the two results: $20 + 1536 = 1556$ .

Thus, the answer is: $1556$ .

Final Answer

$1556$

Key Points to Remember

Essential concepts to master this topic

Order: Calculate square roots and exponents before multiplication and addition
Technique: $\sqrt{16} = 4$ and $8^3 = 512$ first, then multiply
Check: Verify $20 + 1536 = 1556$ by adding step by step ✓

Common Mistakes

Avoid these frequent errors

Adding before completing all multiplications
Don't add 20 + 8³ × 3 = 28 × 3 = 84! This ignores order of operations and gives a drastically wrong result. Always complete all multiplications (20 and 1536) before adding them together.

Practice Quiz

Test your knowledge with interactive questions

$5+\sqrt{36}-1=$

FAQ

Everything you need to know about this question

Why do I calculate the square roots first?

Square roots are like exponents in the order of operations! Following PEMDAS, you calculate $\sqrt{16} = 4$ and $\sqrt{25} = 5$ before any multiplication or addition.

What if I don't know what 8³ equals?

Remember that $8^3 = 8 \times 8 \times 8$ . Calculate step by step: 8 × 8 = 64, then 64 × 8 = 512. Practice common cubes to build speed!

Can I multiply the square roots first or the cube first?

Yes! Since both $\sqrt{16} \times \sqrt{25}$ and $8^3 \times 3$ are separate multiplication groups, you can calculate them in any order. Just don't add until both are complete.

How do I avoid calculation errors with big numbers?

Write each step clearly: $\sqrt{16} \times \sqrt{25} = 4 \times 5 = 20$ , then $8^3 \times 3 = 512 \times 3 = 1536$ , finally $20 + 1536 = 1556$ . Double-check each calculation!

What's the fastest way to check my answer?

Estimate first: $4 \times 5 = 20$ plus $500 \times 3 = 1500$ ≈ 1520
Your answer should be close to 1520
1556 is reasonable! ✓

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